Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is
$-(Q/ 4)(1+ 2\sqrt 2)$
$(Q/ 4)(1+ 2\sqrt 2)$
$-(Q/ 2)(1+ 2\sqrt 2)$
$(Q/ 2)(1+ 2\sqrt 2)$
Electrostatic field of a long uniformly charged wire varies with distance $(r)$ according to relation
If the electric flux entering and leaving an enclosed surface respectively is ${\phi _1}$ and ${\phi _2}$ the electric charge inside the surface will be
An electric dipole of dipole moment $\vec P$ is lying along a uniform electric field $\vec E$ . The work done in rotating the dipole by $90^o$ is
If an insulated non-conducting sphere of radius $R$ has charge density $\rho .$ The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be
A charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the centre of a uniformly charged spherical region of total charge $Q$ and radius $R$. Charges $q$ and $Q$ have opposite signs. The spherically charged region is not free to move and kinetic energy $K$ is just sufficient for the charge particle to reach boundary of the spherical charge. How much time does it take the particle to reach the boundary of the region?